Variations and Generalizations

Abstract

By means of a slight modification every Magic cube can be transformed into a “Supercube”, a puzzle with over 2000 times as many positions. In the first section of this chapter we give a solution for the supercube and a suitable mathematical model. In the second, we pay our respects to an over one hundred year old predecessor of the Rubik’s cube. We present a possibly new and certainly very simple proof of the main theorem of Sam Loyd’s 15-Puzzle. Most of the objects treated in the third section are no longer cube-shaped, but due to a technical and structural kinship, they are all part of our science of cubology: We are talking of magic polyhedrons of all kinds.